A135502 Admirable numbers in the middle of twin primes.

12, 30, 42, 102, 138, 270, 282, 618, 642, 822, 1488, 1698, 1878, 2082, 2238, 2382, 2658, 2802, 3462, 3558, 3918, 4638, 4722, 5442, 6198, 6702, 8538, 8598, 9678, 10938, 12162, 12378, 12822, 12918, 13218, 13722, 13758, 13998, 14082, 16062, 17418

Offset: 1

Author

Olaf Voß, Feb 09 2008

Keywords

• easy
• nonn

Comments

Numbers n such that n is admirable, n-1 is prime and n+1 is prime.

Examples

			30 is in the sequence, as 29=30-1 and 31=30+1 are a pair of twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A111592, A001359, A006512.

Programs

Mathematica

Select[Range[18000],MemberQ[Most[Divisors[#]],(DivisorSigma[1,#]-2#)/2]&&AllTrue[#+{1,-1},PrimeQ]&] (* Harvey P. Dale, Sep 11 2023 *)

Formula

A014574 INTERSECT A111592. - R. J. Mathar, Feb 10 2008